I earned pocket money in college repairing furniture. (fifty years ago) The memories were repressed until I recently stumbled across YouTube videos of a fellow doing the same things. When I think of doing the repairs now, after a few seconds I go, NO!
I would try to determine if that top is veneer. If it is, any of the techniques suggested for soaking it with (whatever) might loosen the veneer. Sanding might sand through and probably would before you got all of the stain out. If it's solid teak you have a chance.
I might contact Thomas Johnson in Gorham Maine. The fellow I have been watching, and see if he has any suggestions. There is much to learn by watching him work.